The eta photon-production reaction on nuclei is studied by employing N* (1535) resonance model. The parameters of the model are extracted by using experimental data of N* decay channels and fitting gammap --> etap reaction cross section. The result shows that the theoretical values are in good agreement with experimental data if M-N* = 1550MeV. The total cross section of the eta photoproduction on C-12 is calculated. We find that the width of N* (1535) in nuclei increases because of corrections of many-body effects, and the interaction between N* and nuclei has the feature of repulsion.